Mismatched fiber optic interferometers are used as the sensing elements for fiber optic acoustic arrays. Each fiber optic interferometer produces a signal S(t) which is a function of the time-varying propagation time difference .tau. for the two paths of the interferometer. EQU S(t)=A(t)+B(t) cos {[.omega..sub.c t+.theta.(t)]-[.omega..sub.c (t-.tau.)+.theta.(t-.tau.)]} (1)
or EQU S(t)=A(t)+B(t) cos [.omega..sub.c .tau.+.theta.(t)-.theta.(t-.tau.)](2)
The quantity A(t) is proportional to the average input optical power to the interferometer, and B(t) is proportional to the average input optical power and also the mixing efficiency of the interferometer. The angular frequency of the input light beam to the interferometer is .omega..sub.c, and .theta.(t) is the phase modulation of the light beam entering the interferometer. The phase modulation aids in the extraction of a measure of the propagation time difference .omega..sub.c .tau..
The extraction of the propagation time difference measure is typically accomplished utilizing a sinusoidally varying .theta.(t) at some carrier frequency produced by either internal frequency modulation of a laser source or by phase modulation with a phase modulator following the laser source. The interferometer output signal consists of a sum of terms involving the various harmonics of the carrier frequency. Mixing of the interferometer signal with appropriate reference signals at harmonics of the carrier frequency and subsequent filtering produces quadrature and inphase outputs at baseband: EQU Q=Q.sub.o sin .omega..sub.c .tau.I=I.sub.o cos .omega..sub.c .tau.(3)
An arctangent operation on the ratio (Q/I)/(Q.sub.0 /I.sub.0)yields the desired quantity.
A digital alternative to the analog extraction approach described above is needed in order to improve the noise, bandwidth, and dynamic range performance of fiber optic acoustic arrays.